# Properties

 Label 576.4.a.h.1.1 Level $576$ Weight $4$ Character 576.1 Self dual yes Analytic conductor $33.985$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,4,Mod(1,576)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("576.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 576.a (trivial)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$33.9851001633$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 32) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 576.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-10.0000 q^{5} +16.0000 q^{7} +O(q^{10})$$ $$q-10.0000 q^{5} +16.0000 q^{7} -40.0000 q^{11} +50.0000 q^{13} +30.0000 q^{17} -40.0000 q^{19} -48.0000 q^{23} -25.0000 q^{25} -34.0000 q^{29} +320.000 q^{31} -160.000 q^{35} -310.000 q^{37} -410.000 q^{41} -152.000 q^{43} +416.000 q^{47} -87.0000 q^{49} -410.000 q^{53} +400.000 q^{55} -200.000 q^{59} -30.0000 q^{61} -500.000 q^{65} -776.000 q^{67} -400.000 q^{71} -630.000 q^{73} -640.000 q^{77} -1120.00 q^{79} +552.000 q^{83} -300.000 q^{85} +326.000 q^{89} +800.000 q^{91} +400.000 q^{95} -110.000 q^{97} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −10.0000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ 16.0000 0.863919 0.431959 0.901893i $$-0.357822\pi$$
0.431959 + 0.901893i $$0.357822\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −40.0000 −1.09640 −0.548202 0.836346i $$-0.684688\pi$$
−0.548202 + 0.836346i $$0.684688\pi$$
$$12$$ 0 0
$$13$$ 50.0000 1.06673 0.533366 0.845885i $$-0.320927\pi$$
0.533366 + 0.845885i $$0.320927\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 30.0000 0.428004 0.214002 0.976833i $$-0.431350\pi$$
0.214002 + 0.976833i $$0.431350\pi$$
$$18$$ 0 0
$$19$$ −40.0000 −0.482980 −0.241490 0.970403i $$-0.577636\pi$$
−0.241490 + 0.970403i $$0.577636\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −48.0000 −0.435161 −0.217580 0.976042i $$-0.569816\pi$$
−0.217580 + 0.976042i $$0.569816\pi$$
$$24$$ 0 0
$$25$$ −25.0000 −0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −34.0000 −0.217712 −0.108856 0.994058i $$-0.534719\pi$$
−0.108856 + 0.994058i $$0.534719\pi$$
$$30$$ 0 0
$$31$$ 320.000 1.85399 0.926995 0.375073i $$-0.122383\pi$$
0.926995 + 0.375073i $$0.122383\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −160.000 −0.772712
$$36$$ 0 0
$$37$$ −310.000 −1.37740 −0.688698 0.725048i $$-0.741818\pi$$
−0.688698 + 0.725048i $$0.741818\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −410.000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ −152.000 −0.539065 −0.269532 0.962991i $$-0.586869\pi$$
−0.269532 + 0.962991i $$0.586869\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 416.000 1.29106 0.645530 0.763735i $$-0.276636\pi$$
0.645530 + 0.763735i $$0.276636\pi$$
$$48$$ 0 0
$$49$$ −87.0000 −0.253644
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −410.000 −1.06260 −0.531300 0.847184i $$-0.678296\pi$$
−0.531300 + 0.847184i $$0.678296\pi$$
$$54$$ 0 0
$$55$$ 400.000 0.980654
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −200.000 −0.441318 −0.220659 0.975351i $$-0.570821\pi$$
−0.220659 + 0.975351i $$0.570821\pi$$
$$60$$ 0 0
$$61$$ −30.0000 −0.0629690 −0.0314845 0.999504i $$-0.510023\pi$$
−0.0314845 + 0.999504i $$0.510023\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −500.000 −0.954113
$$66$$ 0 0
$$67$$ −776.000 −1.41498 −0.707489 0.706725i $$-0.750172\pi$$
−0.707489 + 0.706725i $$0.750172\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −400.000 −0.668609 −0.334305 0.942465i $$-0.608501\pi$$
−0.334305 + 0.942465i $$0.608501\pi$$
$$72$$ 0 0
$$73$$ −630.000 −1.01008 −0.505041 0.863096i $$-0.668522\pi$$
−0.505041 + 0.863096i $$0.668522\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −640.000 −0.947205
$$78$$ 0 0
$$79$$ −1120.00 −1.59506 −0.797531 0.603278i $$-0.793861\pi$$
−0.797531 + 0.603278i $$0.793861\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 552.000 0.729998 0.364999 0.931008i $$-0.381069\pi$$
0.364999 + 0.931008i $$0.381069\pi$$
$$84$$ 0 0
$$85$$ −300.000 −0.382818
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 326.000 0.388269 0.194134 0.980975i $$-0.437810\pi$$
0.194134 + 0.980975i $$0.437810\pi$$
$$90$$ 0 0
$$91$$ 800.000 0.921569
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 400.000 0.431991
$$96$$ 0 0
$$97$$ −110.000 −0.115142 −0.0575712 0.998341i $$-0.518336\pi$$
−0.0575712 + 0.998341i $$0.518336\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1098.00 −1.08173 −0.540867 0.841108i $$-0.681904\pi$$
−0.540867 + 0.841108i $$0.681904\pi$$
$$102$$ 0 0
$$103$$ −48.0000 −0.0459183 −0.0229591 0.999736i $$-0.507309\pi$$
−0.0229591 + 0.999736i $$0.507309\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 664.000 0.599919 0.299959 0.953952i $$-0.403027\pi$$
0.299959 + 0.953952i $$0.403027\pi$$
$$108$$ 0 0
$$109$$ 370.000 0.325134 0.162567 0.986698i $$-0.448023\pi$$
0.162567 + 0.986698i $$0.448023\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1490.00 −1.24042 −0.620210 0.784436i $$-0.712953\pi$$
−0.620210 + 0.784436i $$0.712953\pi$$
$$114$$ 0 0
$$115$$ 480.000 0.389219
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 480.000 0.369761
$$120$$ 0 0
$$121$$ 269.000 0.202104
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1500.00 1.07331
$$126$$ 0 0
$$127$$ −1024.00 −0.715475 −0.357737 0.933822i $$-0.616452\pi$$
−0.357737 + 0.933822i $$0.616452\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1160.00 0.773662 0.386831 0.922151i $$-0.373570\pi$$
0.386831 + 0.922151i $$0.373570\pi$$
$$132$$ 0 0
$$133$$ −640.000 −0.417256
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −570.000 −0.355463 −0.177731 0.984079i $$-0.556876\pi$$
−0.177731 + 0.984079i $$0.556876\pi$$
$$138$$ 0 0
$$139$$ 1960.00 1.19601 0.598004 0.801493i $$-0.295961\pi$$
0.598004 + 0.801493i $$0.295961\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −2000.00 −1.16957
$$144$$ 0 0
$$145$$ 340.000 0.194727
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2010.00 −1.10514 −0.552569 0.833467i $$-0.686352\pi$$
−0.552569 + 0.833467i $$0.686352\pi$$
$$150$$ 0 0
$$151$$ −720.000 −0.388032 −0.194016 0.980998i $$-0.562151\pi$$
−0.194016 + 0.980998i $$0.562151\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3200.00 −1.65826
$$156$$ 0 0
$$157$$ −1790.00 −0.909921 −0.454960 0.890512i $$-0.650347\pi$$
−0.454960 + 0.890512i $$0.650347\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −768.000 −0.375943
$$162$$ 0 0
$$163$$ 1208.00 0.580478 0.290239 0.956954i $$-0.406265\pi$$
0.290239 + 0.956954i $$0.406265\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2896.00 −1.34191 −0.670956 0.741497i $$-0.734116\pi$$
−0.670956 + 0.741497i $$0.734116\pi$$
$$168$$ 0 0
$$169$$ 303.000 0.137915
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 750.000 0.329604 0.164802 0.986327i $$-0.447302\pi$$
0.164802 + 0.986327i $$0.447302\pi$$
$$174$$ 0 0
$$175$$ −400.000 −0.172784
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 2280.00 0.952040 0.476020 0.879434i $$-0.342079\pi$$
0.476020 + 0.879434i $$0.342079\pi$$
$$180$$ 0 0
$$181$$ 442.000 0.181512 0.0907558 0.995873i $$-0.471072\pi$$
0.0907558 + 0.995873i $$0.471072\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 3100.00 1.23198
$$186$$ 0 0
$$187$$ −1200.00 −0.469266
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1920.00 0.727363 0.363681 0.931523i $$-0.381520\pi$$
0.363681 + 0.931523i $$0.381520\pi$$
$$192$$ 0 0
$$193$$ −5070.00 −1.89091 −0.945457 0.325746i $$-0.894385\pi$$
−0.945457 + 0.325746i $$0.894385\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1910.00 0.690771 0.345385 0.938461i $$-0.387748\pi$$
0.345385 + 0.938461i $$0.387748\pi$$
$$198$$ 0 0
$$199$$ 2960.00 1.05442 0.527208 0.849736i $$-0.323239\pi$$
0.527208 + 0.849736i $$0.323239\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −544.000 −0.188085
$$204$$ 0 0
$$205$$ 4100.00 1.39686
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1600.00 0.529542
$$210$$ 0 0
$$211$$ −40.0000 −0.0130508 −0.00652539 0.999979i $$-0.502077\pi$$
−0.00652539 + 0.999979i $$0.502077\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1520.00 0.482154
$$216$$ 0 0
$$217$$ 5120.00 1.60170
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1500.00 0.456565
$$222$$ 0 0
$$223$$ 4288.00 1.28765 0.643824 0.765173i $$-0.277347\pi$$
0.643824 + 0.765173i $$0.277347\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −6456.00 −1.88766 −0.943832 0.330425i $$-0.892808\pi$$
−0.943832 + 0.330425i $$0.892808\pi$$
$$228$$ 0 0
$$229$$ 1066.00 0.307613 0.153806 0.988101i $$-0.450847\pi$$
0.153806 + 0.988101i $$0.450847\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5910.00 1.66170 0.830852 0.556494i $$-0.187854\pi$$
0.830852 + 0.556494i $$0.187854\pi$$
$$234$$ 0 0
$$235$$ −4160.00 −1.15476
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3360.00 0.909374 0.454687 0.890651i $$-0.349751\pi$$
0.454687 + 0.890651i $$0.349751\pi$$
$$240$$ 0 0
$$241$$ 3970.00 1.06112 0.530561 0.847647i $$-0.321981\pi$$
0.530561 + 0.847647i $$0.321981\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 870.000 0.226866
$$246$$ 0 0
$$247$$ −2000.00 −0.515210
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 6840.00 1.72007 0.860034 0.510237i $$-0.170442\pi$$
0.860034 + 0.510237i $$0.170442\pi$$
$$252$$ 0 0
$$253$$ 1920.00 0.477112
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −4610.00 −1.11893 −0.559463 0.828855i $$-0.688993\pi$$
−0.559463 + 0.828855i $$0.688993\pi$$
$$258$$ 0 0
$$259$$ −4960.00 −1.18996
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4848.00 1.13666 0.568328 0.822802i $$-0.307591\pi$$
0.568328 + 0.822802i $$0.307591\pi$$
$$264$$ 0 0
$$265$$ 4100.00 0.950419
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 5550.00 1.25795 0.628977 0.777424i $$-0.283474\pi$$
0.628977 + 0.777424i $$0.283474\pi$$
$$270$$ 0 0
$$271$$ −480.000 −0.107594 −0.0537969 0.998552i $$-0.517132\pi$$
−0.0537969 + 0.998552i $$0.517132\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1000.00 0.219281
$$276$$ 0 0
$$277$$ −1030.00 −0.223418 −0.111709 0.993741i $$-0.535632\pi$$
−0.111709 + 0.993741i $$0.535632\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3270.00 0.694206 0.347103 0.937827i $$-0.387165\pi$$
0.347103 + 0.937827i $$0.387165\pi$$
$$282$$ 0 0
$$283$$ −2168.00 −0.455386 −0.227693 0.973733i $$-0.573118\pi$$
−0.227693 + 0.973733i $$0.573118\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6560.00 −1.34921
$$288$$ 0 0
$$289$$ −4013.00 −0.816813
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2070.00 0.412733 0.206366 0.978475i $$-0.433836\pi$$
0.206366 + 0.978475i $$0.433836\pi$$
$$294$$ 0 0
$$295$$ 2000.00 0.394727
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −2400.00 −0.464199
$$300$$ 0 0
$$301$$ −2432.00 −0.465708
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 300.000 0.0563211
$$306$$ 0 0
$$307$$ −1896.00 −0.352477 −0.176238 0.984347i $$-0.556393\pi$$
−0.176238 + 0.984347i $$0.556393\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1680.00 0.306315 0.153158 0.988202i $$-0.451056\pi$$
0.153158 + 0.988202i $$0.451056\pi$$
$$312$$ 0 0
$$313$$ 970.000 0.175168 0.0875841 0.996157i $$-0.472085\pi$$
0.0875841 + 0.996157i $$0.472085\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 7230.00 1.28100 0.640500 0.767958i $$-0.278727\pi$$
0.640500 + 0.767958i $$0.278727\pi$$
$$318$$ 0 0
$$319$$ 1360.00 0.238700
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1200.00 −0.206718
$$324$$ 0 0
$$325$$ −1250.00 −0.213346
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 6656.00 1.11537
$$330$$ 0 0
$$331$$ 5800.00 0.963132 0.481566 0.876410i $$-0.340068\pi$$
0.481566 + 0.876410i $$0.340068\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 7760.00 1.26559
$$336$$ 0 0
$$337$$ −1870.00 −0.302271 −0.151136 0.988513i $$-0.548293\pi$$
−0.151136 + 0.988513i $$0.548293\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −12800.0 −2.03272
$$342$$ 0 0
$$343$$ −6880.00 −1.08305
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 376.000 0.0581693 0.0290846 0.999577i $$-0.490741\pi$$
0.0290846 + 0.999577i $$0.490741\pi$$
$$348$$ 0 0
$$349$$ 7586.00 1.16352 0.581761 0.813360i $$-0.302364\pi$$
0.581761 + 0.813360i $$0.302364\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −2530.00 −0.381468 −0.190734 0.981642i $$-0.561087\pi$$
−0.190734 + 0.981642i $$0.561087\pi$$
$$354$$ 0 0
$$355$$ 4000.00 0.598022
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −9680.00 −1.42309 −0.711547 0.702638i $$-0.752005\pi$$
−0.711547 + 0.702638i $$0.752005\pi$$
$$360$$ 0 0
$$361$$ −5259.00 −0.766730
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 6300.00 0.903444
$$366$$ 0 0
$$367$$ 2784.00 0.395977 0.197989 0.980204i $$-0.436559\pi$$
0.197989 + 0.980204i $$0.436559\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −6560.00 −0.918001
$$372$$ 0 0
$$373$$ −7910.00 −1.09803 −0.549014 0.835813i $$-0.684997\pi$$
−0.549014 + 0.835813i $$0.684997\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −1700.00 −0.232240
$$378$$ 0 0
$$379$$ −1720.00 −0.233115 −0.116557 0.993184i $$-0.537186\pi$$
−0.116557 + 0.993184i $$0.537186\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −11008.0 −1.46862 −0.734311 0.678813i $$-0.762495\pi$$
−0.734311 + 0.678813i $$0.762495\pi$$
$$384$$ 0 0
$$385$$ 6400.00 0.847206
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −12330.0 −1.60708 −0.803542 0.595248i $$-0.797054\pi$$
−0.803542 + 0.595248i $$0.797054\pi$$
$$390$$ 0 0
$$391$$ −1440.00 −0.186250
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 11200.0 1.42667
$$396$$ 0 0
$$397$$ 4370.00 0.552453 0.276227 0.961093i $$-0.410916\pi$$
0.276227 + 0.961093i $$0.410916\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −3298.00 −0.410709 −0.205354 0.978688i $$-0.565835\pi$$
−0.205354 + 0.978688i $$0.565835\pi$$
$$402$$ 0 0
$$403$$ 16000.0 1.97771
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 12400.0 1.51018
$$408$$ 0 0
$$409$$ −9110.00 −1.10137 −0.550685 0.834713i $$-0.685634\pi$$
−0.550685 + 0.834713i $$0.685634\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −3200.00 −0.381263
$$414$$ 0 0
$$415$$ −5520.00 −0.652930
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 7880.00 0.918767 0.459383 0.888238i $$-0.348070\pi$$
0.459383 + 0.888238i $$0.348070\pi$$
$$420$$ 0 0
$$421$$ 5290.00 0.612396 0.306198 0.951968i $$-0.400943\pi$$
0.306198 + 0.951968i $$0.400943\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −750.000 −0.0856008
$$426$$ 0 0
$$427$$ −480.000 −0.0544001
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −13920.0 −1.55569 −0.777845 0.628456i $$-0.783687\pi$$
−0.777845 + 0.628456i $$0.783687\pi$$
$$432$$ 0 0
$$433$$ 4930.00 0.547161 0.273580 0.961849i $$-0.411792\pi$$
0.273580 + 0.961849i $$0.411792\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1920.00 0.210174
$$438$$ 0 0
$$439$$ −10640.0 −1.15676 −0.578382 0.815766i $$-0.696316\pi$$
−0.578382 + 0.815766i $$0.696316\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −9288.00 −0.996131 −0.498066 0.867139i $$-0.665956\pi$$
−0.498066 + 0.867139i $$0.665956\pi$$
$$444$$ 0 0
$$445$$ −3260.00 −0.347278
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −12850.0 −1.35062 −0.675311 0.737533i $$-0.735990\pi$$
−0.675311 + 0.737533i $$0.735990\pi$$
$$450$$ 0 0
$$451$$ 16400.0 1.71230
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −8000.00 −0.824276
$$456$$ 0 0
$$457$$ 10490.0 1.07375 0.536873 0.843663i $$-0.319606\pi$$
0.536873 + 0.843663i $$0.319606\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 11118.0 1.12325 0.561624 0.827393i $$-0.310177\pi$$
0.561624 + 0.827393i $$0.310177\pi$$
$$462$$ 0 0
$$463$$ 5792.00 0.581376 0.290688 0.956818i $$-0.406116\pi$$
0.290688 + 0.956818i $$0.406116\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2216.00 0.219581 0.109790 0.993955i $$-0.464982\pi$$
0.109790 + 0.993955i $$0.464982\pi$$
$$468$$ 0 0
$$469$$ −12416.0 −1.22243
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 6080.00 0.591033
$$474$$ 0 0
$$475$$ 1000.00 0.0965961
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 10560.0 1.00730 0.503652 0.863907i $$-0.331989\pi$$
0.503652 + 0.863907i $$0.331989\pi$$
$$480$$ 0 0
$$481$$ −15500.0 −1.46931
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 1100.00 0.102986
$$486$$ 0 0
$$487$$ 13264.0 1.23419 0.617094 0.786890i $$-0.288310\pi$$
0.617094 + 0.786890i $$0.288310\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −4840.00 −0.444860 −0.222430 0.974949i $$-0.571399\pi$$
−0.222430 + 0.974949i $$0.571399\pi$$
$$492$$ 0 0
$$493$$ −1020.00 −0.0931815
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −6400.00 −0.577624
$$498$$ 0 0
$$499$$ −19560.0 −1.75476 −0.877381 0.479795i $$-0.840711\pi$$
−0.877381 + 0.479795i $$0.840711\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 528.000 0.0468039 0.0234019 0.999726i $$-0.492550\pi$$
0.0234019 + 0.999726i $$0.492550\pi$$
$$504$$ 0 0
$$505$$ 10980.0 0.967532
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −19554.0 −1.70278 −0.851391 0.524532i $$-0.824240\pi$$
−0.851391 + 0.524532i $$0.824240\pi$$
$$510$$ 0 0
$$511$$ −10080.0 −0.872628
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 480.000 0.0410705
$$516$$ 0 0
$$517$$ −16640.0 −1.41552
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −15162.0 −1.27497 −0.637485 0.770463i $$-0.720025\pi$$
−0.637485 + 0.770463i $$0.720025\pi$$
$$522$$ 0 0
$$523$$ −10968.0 −0.917012 −0.458506 0.888691i $$-0.651615\pi$$
−0.458506 + 0.888691i $$0.651615\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 9600.00 0.793515
$$528$$ 0 0
$$529$$ −9863.00 −0.810635
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −20500.0 −1.66595
$$534$$ 0 0
$$535$$ −6640.00 −0.536584
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3480.00 0.278097
$$540$$ 0 0
$$541$$ 6722.00 0.534198 0.267099 0.963669i $$-0.413935\pi$$
0.267099 + 0.963669i $$0.413935\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −3700.00 −0.290808
$$546$$ 0 0
$$547$$ −20424.0 −1.59647 −0.798233 0.602348i $$-0.794232\pi$$
−0.798233 + 0.602348i $$0.794232\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1360.00 0.105151
$$552$$ 0 0
$$553$$ −17920.0 −1.37800
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −6610.00 −0.502827 −0.251414 0.967880i $$-0.580895\pi$$
−0.251414 + 0.967880i $$0.580895\pi$$
$$558$$ 0 0
$$559$$ −7600.00 −0.575037
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −2712.00 −0.203015 −0.101507 0.994835i $$-0.532367\pi$$
−0.101507 + 0.994835i $$0.532367\pi$$
$$564$$ 0 0
$$565$$ 14900.0 1.10946
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −3530.00 −0.260080 −0.130040 0.991509i $$-0.541511\pi$$
−0.130040 + 0.991509i $$0.541511\pi$$
$$570$$ 0 0
$$571$$ 13640.0 0.999678 0.499839 0.866118i $$-0.333392\pi$$
0.499839 + 0.866118i $$0.333392\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1200.00 0.0870321
$$576$$ 0 0
$$577$$ −6270.00 −0.452380 −0.226190 0.974083i $$-0.572627\pi$$
−0.226190 + 0.974083i $$0.572627\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 8832.00 0.630659
$$582$$ 0 0
$$583$$ 16400.0 1.16504
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −8616.00 −0.605827 −0.302913 0.953018i $$-0.597959\pi$$
−0.302913 + 0.953018i $$0.597959\pi$$
$$588$$ 0 0
$$589$$ −12800.0 −0.895441
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −5490.00 −0.380181 −0.190090 0.981767i $$-0.560878\pi$$
−0.190090 + 0.981767i $$0.560878\pi$$
$$594$$ 0 0
$$595$$ −4800.00 −0.330724
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 15440.0 1.05319 0.526595 0.850116i $$-0.323468\pi$$
0.526595 + 0.850116i $$0.323468\pi$$
$$600$$ 0 0
$$601$$ 8890.00 0.603379 0.301689 0.953406i $$-0.402449\pi$$
0.301689 + 0.953406i $$0.402449\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −2690.00 −0.180767
$$606$$ 0 0
$$607$$ 23744.0 1.58771 0.793854 0.608108i $$-0.208071\pi$$
0.793854 + 0.608108i $$0.208071\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 20800.0 1.37721
$$612$$ 0 0
$$613$$ 15210.0 1.00216 0.501082 0.865400i $$-0.332936\pi$$
0.501082 + 0.865400i $$0.332936\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 12630.0 0.824092 0.412046 0.911163i $$-0.364814\pi$$
0.412046 + 0.911163i $$0.364814\pi$$
$$618$$ 0 0
$$619$$ −11160.0 −0.724650 −0.362325 0.932052i $$-0.618017\pi$$
−0.362325 + 0.932052i $$0.618017\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 5216.00 0.335433
$$624$$ 0 0
$$625$$ −11875.0 −0.760000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −9300.00 −0.589531
$$630$$ 0 0
$$631$$ 13040.0 0.822685 0.411342 0.911481i $$-0.365060\pi$$
0.411342 + 0.911481i $$0.365060\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 10240.0 0.639940
$$636$$ 0 0
$$637$$ −4350.00 −0.270570
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 16910.0 1.04197 0.520987 0.853565i $$-0.325564\pi$$
0.520987 + 0.853565i $$0.325564\pi$$
$$642$$ 0 0
$$643$$ −4488.00 −0.275256 −0.137628 0.990484i $$-0.543948\pi$$
−0.137628 + 0.990484i $$0.543948\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2064.00 −0.125416 −0.0627080 0.998032i $$-0.519974\pi$$
−0.0627080 + 0.998032i $$0.519974\pi$$
$$648$$ 0 0
$$649$$ 8000.00 0.483864
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 4270.00 0.255893 0.127946 0.991781i $$-0.459161\pi$$
0.127946 + 0.991781i $$0.459161\pi$$
$$654$$ 0 0
$$655$$ −11600.0 −0.691984
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −19800.0 −1.17041 −0.585204 0.810886i $$-0.698985\pi$$
−0.585204 + 0.810886i $$0.698985\pi$$
$$660$$ 0 0
$$661$$ −27110.0 −1.59524 −0.797622 0.603157i $$-0.793909\pi$$
−0.797622 + 0.603157i $$0.793909\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 6400.00 0.373205
$$666$$ 0 0
$$667$$ 1632.00 0.0947396
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1200.00 0.0690395
$$672$$ 0 0
$$673$$ 32210.0 1.84488 0.922440 0.386140i $$-0.126192\pi$$
0.922440 + 0.386140i $$0.126192\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 27190.0 1.54357 0.771785 0.635884i $$-0.219364\pi$$
0.771785 + 0.635884i $$0.219364\pi$$
$$678$$ 0 0
$$679$$ −1760.00 −0.0994736
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −20328.0 −1.13884 −0.569421 0.822046i $$-0.692833\pi$$
−0.569421 + 0.822046i $$0.692833\pi$$
$$684$$ 0 0
$$685$$ 5700.00 0.317935
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −20500.0 −1.13351
$$690$$ 0 0
$$691$$ −12520.0 −0.689267 −0.344633 0.938737i $$-0.611997\pi$$
−0.344633 + 0.938737i $$0.611997\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −19600.0 −1.06974
$$696$$ 0 0
$$697$$ −12300.0 −0.668430
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 11550.0 0.622307 0.311154 0.950360i $$-0.399285\pi$$
0.311154 + 0.950360i $$0.399285\pi$$
$$702$$ 0 0
$$703$$ 12400.0 0.665256
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −17568.0 −0.934530
$$708$$ 0 0
$$709$$ 34154.0 1.80914 0.904570 0.426325i $$-0.140192\pi$$
0.904570 + 0.426325i $$0.140192\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −15360.0 −0.806783
$$714$$ 0 0
$$715$$ 20000.0 1.04609
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 22880.0 1.18676 0.593380 0.804923i $$-0.297793\pi$$
0.593380 + 0.804923i $$0.297793\pi$$
$$720$$ 0 0
$$721$$ −768.000 −0.0396696
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 850.000 0.0435424
$$726$$ 0 0
$$727$$ 10416.0 0.531373 0.265686 0.964060i $$-0.414401\pi$$
0.265686 + 0.964060i $$0.414401\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −4560.00 −0.230722
$$732$$ 0 0
$$733$$ −14750.0 −0.743252 −0.371626 0.928383i $$-0.621200\pi$$
−0.371626 + 0.928383i $$0.621200\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 31040.0 1.55139
$$738$$ 0 0
$$739$$ 2360.00 0.117475 0.0587375 0.998273i $$-0.481293\pi$$
0.0587375 + 0.998273i $$0.481293\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −32208.0 −1.59031 −0.795153 0.606409i $$-0.792609\pi$$
−0.795153 + 0.606409i $$0.792609\pi$$
$$744$$ 0 0
$$745$$ 20100.0 0.988466
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 10624.0 0.518281
$$750$$ 0 0
$$751$$ −36640.0 −1.78031 −0.890155 0.455658i $$-0.849404\pi$$
−0.890155 + 0.455658i $$0.849404\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 7200.00 0.347066
$$756$$ 0 0
$$757$$ 12090.0 0.580474 0.290237 0.956955i $$-0.406266\pi$$
0.290237 + 0.956955i $$0.406266\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 3318.00 0.158052 0.0790259 0.996873i $$-0.474819\pi$$
0.0790259 + 0.996873i $$0.474819\pi$$
$$762$$ 0 0
$$763$$ 5920.00 0.280889
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −10000.0 −0.470768
$$768$$ 0 0
$$769$$ 11506.0 0.539554 0.269777 0.962923i $$-0.413050\pi$$
0.269777 + 0.962923i $$0.413050\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 22230.0 1.03436 0.517178 0.855878i $$-0.326982\pi$$
0.517178 + 0.855878i $$0.326982\pi$$
$$774$$ 0 0
$$775$$ −8000.00 −0.370798
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 16400.0 0.754289
$$780$$ 0 0
$$781$$ 16000.0 0.733067
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 17900.0 0.813858
$$786$$ 0 0
$$787$$ 21336.0 0.966387 0.483193 0.875514i $$-0.339477\pi$$
0.483193 + 0.875514i $$0.339477\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −23840.0 −1.07162
$$792$$ 0 0
$$793$$ −1500.00 −0.0671709
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −7170.00 −0.318663 −0.159332 0.987225i $$-0.550934\pi$$
−0.159332 + 0.987225i $$0.550934\pi$$
$$798$$ 0 0
$$799$$ 12480.0 0.552579
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 25200.0 1.10746
$$804$$ 0 0
$$805$$ 7680.00 0.336254
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 23654.0 1.02797 0.513987 0.857798i $$-0.328168\pi$$
0.513987 + 0.857798i $$0.328168\pi$$
$$810$$ 0 0
$$811$$ 30440.0 1.31799 0.658997 0.752146i $$-0.270981\pi$$
0.658997 + 0.752146i $$0.270981\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −12080.0 −0.519195
$$816$$ 0 0
$$817$$ 6080.00 0.260358
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −19930.0 −0.847213 −0.423606 0.905846i $$-0.639236\pi$$
−0.423606 + 0.905846i $$0.639236\pi$$
$$822$$ 0 0
$$823$$ −9872.00 −0.418124 −0.209062 0.977902i $$-0.567041\pi$$
−0.209062 + 0.977902i $$0.567041\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −5704.00 −0.239840 −0.119920 0.992784i $$-0.538264\pi$$
−0.119920 + 0.992784i $$0.538264\pi$$
$$828$$ 0 0
$$829$$ −27230.0 −1.14082 −0.570408 0.821361i $$-0.693215\pi$$
−0.570408 + 0.821361i $$0.693215\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2610.00 −0.108561
$$834$$ 0 0
$$835$$ 28960.0 1.20024
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 18800.0 0.773597 0.386799 0.922164i $$-0.373581\pi$$
0.386799 + 0.922164i $$0.373581\pi$$
$$840$$ 0 0
$$841$$ −23233.0 −0.952602
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −3030.00 −0.123355
$$846$$ 0 0
$$847$$ 4304.00 0.174601
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 14880.0 0.599389
$$852$$ 0 0
$$853$$ 12090.0 0.485292 0.242646 0.970115i $$-0.421985\pi$$
0.242646 + 0.970115i $$0.421985\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 470.000 0.0187338 0.00936692 0.999956i $$-0.497018\pi$$
0.00936692 + 0.999956i $$0.497018\pi$$
$$858$$ 0 0
$$859$$ −24440.0 −0.970759 −0.485380 0.874304i $$-0.661319\pi$$
−0.485380 + 0.874304i $$0.661319\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 22592.0 0.891125 0.445562 0.895251i $$-0.353004\pi$$
0.445562 + 0.895251i $$0.353004\pi$$
$$864$$ 0 0
$$865$$ −7500.00 −0.294807
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 44800.0 1.74883
$$870$$ 0 0
$$871$$ −38800.0 −1.50940
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 24000.0 0.927255
$$876$$ 0 0
$$877$$ 17330.0 0.667266 0.333633 0.942703i $$-0.391725\pi$$
0.333633 + 0.942703i $$0.391725\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 31470.0 1.20346 0.601732 0.798698i $$-0.294478\pi$$
0.601732 + 0.798698i $$0.294478\pi$$
$$882$$ 0 0
$$883$$ 3352.00 0.127751 0.0638753 0.997958i $$-0.479654\pi$$
0.0638753 + 0.997958i $$0.479654\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 48144.0 1.82245 0.911227 0.411904i $$-0.135136\pi$$
0.911227 + 0.411904i $$0.135136\pi$$
$$888$$ 0 0
$$889$$ −16384.0 −0.618112
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −16640.0 −0.623557
$$894$$ 0 0
$$895$$ −22800.0 −0.851531
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −10880.0 −0.403636
$$900$$ 0 0
$$901$$ −12300.0 −0.454797
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −4420.00 −0.162349
$$906$$ 0 0
$$907$$ −16216.0 −0.593653 −0.296827 0.954931i $$-0.595928\pi$$
−0.296827 + 0.954931i $$0.595928\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −49440.0 −1.79805 −0.899023 0.437901i $$-0.855722\pi$$
−0.899023 + 0.437901i $$0.855722\pi$$
$$912$$ 0 0
$$913$$ −22080.0 −0.800374
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 18560.0 0.668381
$$918$$ 0 0
$$919$$ −16080.0 −0.577182 −0.288591 0.957452i $$-0.593187\pi$$
−0.288591 + 0.957452i $$0.593187\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −20000.0 −0.713226
$$924$$ 0 0
$$925$$ 7750.00 0.275479
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 11310.0 0.399428 0.199714 0.979854i $$-0.435999\pi$$
0.199714 + 0.979854i $$0.435999\pi$$
$$930$$ 0 0
$$931$$ 3480.00 0.122505
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 12000.0 0.419724
$$936$$ 0 0
$$937$$ 25130.0 0.876159 0.438080 0.898936i $$-0.355659\pi$$
0.438080 + 0.898936i $$0.355659\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −22322.0 −0.773301 −0.386651 0.922226i $$-0.626368\pi$$
−0.386651 + 0.922226i $$0.626368\pi$$
$$942$$ 0 0
$$943$$ 19680.0 0.679607
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 36456.0 1.25096 0.625481 0.780239i $$-0.284903\pi$$
0.625481 + 0.780239i $$0.284903\pi$$
$$948$$ 0 0
$$949$$ −31500.0 −1.07749
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −40650.0 −1.38172 −0.690862 0.722987i $$-0.742769\pi$$
−0.690862 + 0.722987i $$0.742769\pi$$
$$954$$ 0 0
$$955$$ −19200.0 −0.650573
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −9120.00 −0.307091
$$960$$ 0 0
$$961$$ 72609.0 2.43728
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 50700.0 1.69129
$$966$$ 0 0
$$967$$ 34704.0 1.15409 0.577045 0.816712i $$-0.304206\pi$$
0.577045 + 0.816712i $$0.304206\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −30760.0 −1.01662 −0.508309 0.861175i $$-0.669729\pi$$
−0.508309 + 0.861175i $$0.669729\pi$$
$$972$$ 0 0
$$973$$ 31360.0 1.03325
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 38110.0 1.24795 0.623975 0.781444i $$-0.285517\pi$$
0.623975 + 0.781444i $$0.285517\pi$$
$$978$$ 0 0
$$979$$ −13040.0 −0.425700
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −19632.0 −0.636992 −0.318496 0.947924i $$-0.603178\pi$$
−0.318496 + 0.947924i $$0.603178\pi$$
$$984$$ 0 0
$$985$$ −19100.0 −0.617844
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 7296.00 0.234580
$$990$$ 0 0
$$991$$ −47680.0 −1.52836 −0.764180 0.645003i $$-0.776856\pi$$
−0.764180 + 0.645003i $$0.776856\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −29600.0 −0.943099
$$996$$ 0 0
$$997$$ 39690.0 1.26078 0.630389 0.776280i $$-0.282896\pi$$
0.630389 + 0.776280i $$0.282896\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 576.4.a.h.1.1 1
3.2 odd 2 64.4.a.a.1.1 1
4.3 odd 2 576.4.a.g.1.1 1
8.3 odd 2 288.4.a.h.1.1 1
8.5 even 2 288.4.a.i.1.1 1
12.11 even 2 64.4.a.e.1.1 1
15.14 odd 2 1600.4.a.bw.1.1 1
24.5 odd 2 32.4.a.c.1.1 yes 1
24.11 even 2 32.4.a.a.1.1 1
48.5 odd 4 256.4.b.c.129.2 2
48.11 even 4 256.4.b.e.129.1 2
48.29 odd 4 256.4.b.c.129.1 2
48.35 even 4 256.4.b.e.129.2 2
60.59 even 2 1600.4.a.e.1.1 1
120.29 odd 2 800.4.a.a.1.1 1
120.53 even 4 800.4.c.a.449.2 2
120.59 even 2 800.4.a.k.1.1 1
120.77 even 4 800.4.c.a.449.1 2
120.83 odd 4 800.4.c.b.449.1 2
120.107 odd 4 800.4.c.b.449.2 2
168.83 odd 2 1568.4.a.o.1.1 1
168.125 even 2 1568.4.a.c.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.a.a.1.1 1 24.11 even 2
32.4.a.c.1.1 yes 1 24.5 odd 2
64.4.a.a.1.1 1 3.2 odd 2
64.4.a.e.1.1 1 12.11 even 2
256.4.b.c.129.1 2 48.29 odd 4
256.4.b.c.129.2 2 48.5 odd 4
256.4.b.e.129.1 2 48.11 even 4
256.4.b.e.129.2 2 48.35 even 4
288.4.a.h.1.1 1 8.3 odd 2
288.4.a.i.1.1 1 8.5 even 2
576.4.a.g.1.1 1 4.3 odd 2
576.4.a.h.1.1 1 1.1 even 1 trivial
800.4.a.a.1.1 1 120.29 odd 2
800.4.a.k.1.1 1 120.59 even 2
800.4.c.a.449.1 2 120.77 even 4
800.4.c.a.449.2 2 120.53 even 4
800.4.c.b.449.1 2 120.83 odd 4
800.4.c.b.449.2 2 120.107 odd 4
1568.4.a.c.1.1 1 168.125 even 2
1568.4.a.o.1.1 1 168.83 odd 2
1600.4.a.e.1.1 1 60.59 even 2
1600.4.a.bw.1.1 1 15.14 odd 2